Brane Surface Research Articles

Hydrogen-like spectrum of spontaneously created brane universes with de-Sitter ground state

Unification of Randall–Sundrum and Regge–Teitelboim brane cosmologies gives birth to a serendipitous Higgs–deSitter interplay. A localized Dvali–Gabadadze–Porrati scalar field, governed by a particular (analytically derived) double-well quartic potential, becomes a mandatory ingredient for supporting a deSitter brane universe. When upgraded to a general Higgs potential, the brane surface tension gets quantized, resembling a Hydrogen atom spectrum, with deSitter universe serving as the ground state. This reflects the local/global structure of the Euclidean manifold: From finite energy density no-boundary initial conditions, via a novel acceleration divide filter, to exact matching conditions at the exclusive nucleation point. Imaginary time periodicity comes as a bonus, with the associated Hawking temperature vanishing at the continuum limit. Upon spontaneous creation, while a finite number of levels describe universes dominated by a residual dark energy combined with damped matter oscillations, an infinite tower of excited levels undergo a Big Crunch.

Prediction of power consumption and performance in ultrafiltration of simulated latex effluent using non-uniform pore sized membranes

Tha aim of the present study was to develop a series of numerical models for an accurate prediction of the power consumption in ultrafiltration of simulated latex effluent. The developed power consumption model incorporated fouling attachment, as well as chemical and physical factors in membrane fouling, in order to ensure accurate prediction and scale-up. This model was applied to heterogeneous membranes with non-uniform pore sizes at a given operating conditions and mem- brane surface charges. Polysulfone flat membrane, with a membrane molecular weight cutoff (MWCO) of 60,000 dalton, at different surface charges was used under a constant flow rate and cross-flow mode. In addition, the developed models were examined using various membranes at a variety of surface charges so as to test the overall reliability and accuracy of these models. The power consumption predicted by the models corresponded to the calculated values from the experimental data for various hydrophilic and hydrophobic membranes with an error margin of 6.0% up to 19.1%.

Anomaly inflow and membrane dynamics in the QCD vacuum

Large ${N}_{c}$ and holographic arguments, as well as Monte Carlo results, suggest that the topological structure of the QCD vacuum is dominated by codimension-one membranes which appear as thin dipole layers of topological charge. Such membranes arise naturally as $D6$-branes in the holographic formulation of QCD based on IIA string theory. The polarizability of these membranes leads to a vacuum energy $\ensuremath{\propto}{\ensuremath{\theta}}^{2}$, providing the origin of nonzero topological susceptibility. Here we show that the axial U(1) anomaly can be formulated as anomaly inflow on the brane surfaces. A 4D gauge transformation at the brane surface separates into a 3D gauge transformation of components within the brane and the transformation of the transverse component. The in-brane gauge transformation induces currents of an effective Chern-Simons theory on the brane surface, while the transformation of the transverse component describes the transverse motion of the brane and is related to the Ramond-Ramond closed string field in the holographic formulation of QCD. The relation between the surface currents and the transverse motion of the brane is dictated by the descent equations of Yang-Mills theory.

Asymptotic solution of the Nernst-Planck-Poisson-Stokes set near a surface with selective properties

The asymptotic approach (5) to the solution of a twodimensional problem taking into account the hydrodynamics is based, in particular, on the assump� tion that the variation of unknowns along the mem� brane surface is slow in comparison with the variations along the transverse direction. In (5) the assumptions (3) were used and the expression for the slippage veloc� ity at the region boundary with the subsequent use of this expression for solving the problem in the electri� cally neutral diffusion region is obtained. Such an approach proved to be incorrect. In (4) the solution was corrected by taking into account the effect of nar� row boundary layers. The assumption about the slow� ness of variations along the membrane was left without change.

Black holes in the brane world: Some exact solutions

We briefly review methods for and results from constructing multidimensional solutions with an event horizon generated by matter localized on a brane. We investigate a particular exact solution of the black star type with the Schwarzschild-Tangherlini geometry in the bulk. We study the extrinsic curvature tensor, which predicts the matter distribution on the brane in accordance with the Israel conditions. We calculate all components of the four-dimensional Riemann tensor describing the intrinsic geometry on the brane surface and also investigate their asymptotic forms at a large distance from the center, limits on the horizon, and the asymptotic forms in the singularity neighborhood of a five-dimensional black hole in the case where the brane intersects it.

Gravitational field equations in a braneworld with Euler–Poincaré term

We present the effective gravitational field equations in a 3-braneworld with Euler–Poincaré term and a cosmological constant in the bulk spacetime. The similar equations on a 3-brane with symmetry embedded in a five-dimensional bulk spacetime were obtained earlier by Maeda and Torii using the Gauss–Codazzi projective approach in the framework of the Gaussian normal coordinates. We recover these equations on the brane in terms of differential forms and using a more general coordinate setting in the manner of Arnowitt, Deser and Misner (ADM). The latter allows for acceleration of the normals to the brane surface through the lapse function and the shift vector. We show that the gravitational effects of the bulk space are transmitted to the brane through the projected ‘electric’ 1-form field constructed from the conformal Weyl curvature 2-form of the bulk space. We also derive the evolution equations into the bulk space for the electric 1-form field, as well as for the ‘magnetic’ 2-form field parts of the bulk Riemann curvature 2-form. As expected, unlike on-brane equations, the evolution equations involve terms determined by the nonvanishing acceleration of the normals in the ADM-type slicing of spacetime.

Radiation Back-Reaction and Renormalization in Classical Field Theory with Singular Sources

We propose a general covariant method for regularizing the radiation back-reaction in linear and nonlinear field theory models with singular sources. Typical examples of such sources are the currents produced by extended relativistic objects (branes). As an illustration, we consider the models of minimal and nonminimal coupling of a brane to an n-form gauge field, a scalar field, and the Einstein gravity field. We find the structure of divergent and finite contributions due to the radiation back-reaction and obtain relations for the parameters of the theory ensuring cancellation of divergences. We prove that the divergences are Lagrangian n the case where the metric induced on the brane surface is nondegenerate. We find special types of a (nonminimal) coupling leading to local and Lagrangian effective equations of motion of the brane. We show that the requirement for classical renormalizability imposes strong restrictions on the self-coupling vertices of the field, similar to the quantum renormalizability conditions. In particular, we establish the nonrenormalizability of the gravitational self-coupling of a codimension-(k>2) brane, whereas for k ≤ 2, the theory becomes not only renormalizable but also finite.

Gravitational field equations on and off a 3-brane world

The effective gravitational field equations on and off a 3-brane world possessing a mirror symmetry and embedded in a five-dimensional bulk spacetime with cosmological constant were derived by Shiromizu, Maeda and Sasaki (SMS) in the framework of the Gauss–Codazzi projective approach with the subsequent specialization to the Gaussian normal coordinates in the neighbourhood of the brane. However, the Gaussian normal coordinates imply a very special slicing of spacetime and clearly, the consistent analysis of the brane dynamics would benefit from complete freedom in the slicing of spacetime, pushing the layer surfaces in the fifth dimension at any rates of evolution and in arbitrary positions. We rederive the SMS effective gravitational field equations on a 3-brane and generalize the off-brane equations to the case where there is an arbitrary energy–momentum tensor in the bulk. We use a more general setting to allow for acceleration of the normals to the brane surface through the lapse function and the shift vector in the spirit of Arnowitt, Deser and Misner. We show that the gravitational influence of the bulk spacetime on the brane may be described by a traceless second-rank tensor , constructed from the ‘electric’ part of the bulk Riemann tensor. We also present the evolution equations for the tensor , as well as for the corresponding ‘magnetic’ part of the bulk curvature. These equations involve terms determined by both the nonvanishing acceleration of normals in the nongeodesic slicing of spacetime and the presence of other fields in the bulk.

Gradient Formula for Linearly Self-Interacting Branes

The computation of long range linear self-interaction forces in string and higher dimensional brane models requires the evaluation of the gradients of regularised values of divergent self-interaction potentials. It is shown that the appropriately regularised gradient in directions orthogonal to the brane surface will always be obtainable simply by multiplying the regularised potential components by just half the trace of the second fundamental tensor, except in the hypermembrane case for which the method fails. Whatever the dimension of the background this result is valid provided the codimension is two (the hyperstring case) or more, so it can be used for investigating brane-world scenarios with more than one extra space dimension.

Non-conservation of global charges in the Brane Universe and baryogenesis

We argue that global charges, such as baryon or lepton number, are not conserved in theories with the Standard Model fields localized on the brane which propagates in higher-dimensional space-time. The global-charge non-conservation is due to quantum fluctuations of the brane surface. These fluctuations create “baby branes” that can capture some global charges and carry them away into the bulk of higher-dimensional space. Such processes are exponentially suppressed at low-energies, but can be significant at high enough temperatures or energies. These effects can lead to a new, intrinsically high-dimensional mechanism of baryogenesis. Baryon asymmetry might be produced due either to “evaporation” into the baby branes, or creation of the baryon number excess in collisions of two Brane Universes. As an example we discuss a possible cosmological scenario within the recently proposed “Brane Inflation” framework. Inflation is driven by displaced branes which slowly fall on top of each other. When the branes collide inflation stops and the Brane Universe reheats. During this non-equilibrium collision baryon number can be transported from one brane to another one. This results in the baryon number excess in our Universe which exactly equals to the hidden “baryon number” deficit in the other Brane Universe.

Wall shear stress: effective parameter for the characterisation of the cross-flow transport in turbulent regime during skimmed milk microfiltration

Sorne experimental evidence is accumulating in the literature which shows that the mean cross-flow velocity is not an effective parame ter for the characterisation of the cross-flow transport in membrane separation processes. The aim of this work was to determine the most appro- priate parameters (among the wall shear stress, tw' the wall shear rate, y, the Reynolds number, Re, and the mean cross-flow velocity, v) that should be used to assess the limiting and critical fluxes in turbulent regime. The experiments were applied to skimmed milk microfiitration (MF) using a tubu- Jar ceramic membrane (0.1 IJ.m mean pore diameter) for the separation of casein micelles from the solluble proteins. These experiments were conducted with several membrane geometries (seven or 19 channel s, 40 or 85.6 cm long) and seve rai rigs. Unlike Re and v, tw made it possible to assess the Iimiting and critical permeation fluxes in milk MF (0.1 IJ.m),whatever the membrane geometry. It was consequently concluded to be an effective parameter to account for cake filtration and to study the cross- flow filtration scale-up. The wall shear rate, calculated by assuming the turbulence damped at the mem- brane surface and the flow laminar, was not suitable for the assessment of the Iimiting and critical fluxes in turbulent regime. © Inra/Elsevier, Paris. wall shear stress / hydrodynamics / critical permeation flux / cross-flow microfiltration / skimmed milk

In situ electrophoresis of membrane components.

During the past decade, the realization that cell membrane constituents may exist in a fluid matrix, each constituent capable of exhibiting rapid rotational and translational motions within the membrane (20, 70), has not only reshaped our concepts about the structure and function of the cell membrane, but also has brought about a number of new problems in membrane biology. The interactions among membrane components (25), mobilities of lipids and proteins (20, 49), and mechanisms for stabilizing and modulating membrane topography (19, 47, 48) are some of the subjects currently under extensive investigation. One ap­ proach to these problems is to perturb experimentally the steady state topography of the membrane components and then examine the struct­ ural and functional consequences of such a perturbation. In situ elec­ trophoresis is one of the newly developed methods in this experimental approach. It is based on the idea that charged membrane components, if free to move laterally in the plane of the membrane, should undergo redistribution in response to an electric field applied along the mem­ brane surface. This lateral in cell membranes was first suggested by Jaffe as a possible cellular mechanism underlying the effects of biogenic electric field in developing systems (31). The study of in situ electrophoresis of membrane components is still in a state of infancy. Only half a dozen publications have appeared since the first reports in 1977 (31, 61). Thus, the purpose of the present paper is not simply to review this relatively scarce and recent literature but to provide a concise theoretical framework for the use of in situ electrophoresis, to summarize lessons learned in the experimental stud­ ies, and to point out possible strategies for the application of this